In addition to reasons already noted, if one gate is staged for a flight, in terms of bags, cargo, pax, etc. it's not always possible (or easy) to just put another plane there. This is why, in ATL for example, you might not be able to get to your original gate (if a plane is still there) but you can't just pull into any open gate. Also could explain why you might hold out for a plane to leave, if it's determined that the wait would be faster then reassigning & moving to another gate.

Not every plane can fit at every gate.

In ATL there are 'gate keepers' in the ramp towers who make such decisions, with the help of the tower agent handling the flight that has to move and possibly with input from maintenance or other departments depending on the reasons a gate swap is needed. Other factors considered include available aircraft to make a swap if that's necessary, GA(s) to handle the new gate, getting ramp personnel to the new gate, moving outbound pax/crew and the potential domino effect to other flights impacted, etc.

Swapping destinations on two planes isn't necessarily easy either, but can be done.

For example: I recall a mid-morning flight ATL-DFW & our inbound plane arrived with a maintenance issue. They announced...we're either delayed until 1:00 or moving to another gate, stand by. About 5 minutes later they moved us to another gate where the same aircraft type was available that wasn't scheduled to depart for a couple of hours. It had the exact configuration so the computer/GA didn't even have to re-seat pax. They hedged their bets on getting the mtc issue fixed in time for the later flight, and they were willing to take the extra time to get bags, cargo, etc. moved to the new plane vs a 3+ hour delay on the earlier flight.